Multiperiod Competitive Supply Chain Networks with Inventorying and A Transportation Network Equilibrium Reformulation

Abstract: In this paper, we present a multitiered dynamic supply chain network equilibrium modeling framework in which the decision-makers have sufficient information about the future and seek to determine their optimal plans that maximize their profits over the multiperiod planning horizon. We construct the finite-dimensional variational inequality governing the equilibrium of the multiperiod competitive supply chain network. The model allows us to investigate the interplay of the heterogeneous decision-makers in the supply chain in a dynamic setting, and to compute the resultant equilibrium pattern of product outputs, transactions, inventories, and product prices. We then establish the supernetwork equivalence of the multiperiod supply chain model with a properly configured transportation network, which provides a new interpretation of the equilibrium conditions of the former in terms of paths and path flows. This framework offers great modeling flexibility so that, for example, transportation delay and/or perishable products can be easily handled, as we also demonstrate. Numerical examples are provided to illustrate how such multiperiod supply chain problems can be reformulated and solved as transportation network equilibrium problems in practice.